A153411 - OEIS

%I #6 Mar 17 2016 13:35:01

%S 5,7,29,71,239,509,691,1019,1777,2111,2801,3181,10667,12401,12907,

%T 13499,15161,18587,20593,21893,25391,26249,26683,33617,36791,36947,

%U 41413,41453,43577,61553,63347,63853,68917,72019,75731,76369,76487,86689

%N Larger of 3 consecutive prime numbers such that p1*p2*p3*d1*d2=average of twin prime pairs; p1,p2,p3 consecutive prime numbers; d1(delta)=p2-p1, d2(delta)=p3-p2.

%C 2*3*5*1*2=60+-1=primes, 3*5*7*2*2=420+-1=primes, 19*23*29*4*6=304152+-1=primes,...

%H Harvey P. Dale, <a href="/A153411/b153411.txt">Table of n, a(n) for n = 1..1000</a>

%t lst={};Do[p1=Prime[n];p2=Prime[n+1];p3=Prime[n+2];d1=p2-p1;d2=p3-p2;a=p1*p2*p3*d1*d2;If[PrimeQ[a-1]&&PrimeQ[a+1],AppendTo[lst,p3]],{n,8!}];lst

%t tppQ[n_]:=Module[{c=Times@@Join[n,Differences[n]]},AllTrue[c+{1,-1}, PrimeQ]]; Transpose[Select[Partition[Prime[Range[10^4]],3,1], tppQ]] [[3]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 17 2016 *)

%Y Cf. A099349, A153374, A153375, A153376, A153377, A153378, A153379, A153406, A153407, A153408, A153409, A153410

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 25 2008